Baseline-adjusted proportional odds models for the quantification of treatment effects in trials with ordinal sum score outcomes

Buri, Muriel; Curt, Armin; Steeves, John; Hothorn, Torsten

doi:10.1186/s12874-020-00984-2

Table 1 Statistical power of the UEMS total sum score model M1 for all simulation settings (1:1 allocation) compared with that of conventional approaches

From: Baseline-adjusted proportional odds models for the quantification of treatment effects in trials with ordinal sum score outcomes

Experimental conditions (1:1 allocation)				Novel model-based methods		Conventional approaches
N total	N trtmt	N ctrl	Odds ratio	Asymptotic ePolr test based on model M1	Permutated ePolr test based on model M1	t-test M1	Wilcoxon rank sum test M1	ANCOVA M1
80	40	40	1.00	.062 [.058,.067]	.049 [.045,.052]	.049 [.046,.053]	.049 [.045,.052]	.048 [.045,.052]
120	60	60	1.00	.061 [.057,.065]	.050 [.046,.053]	.053 [.049,.056]	.050 [.046,.053]	.052 [.049,.056]
160	80	80	1.00	.058 [.054,.062]	.046 [.042,.049]	.049 [.046,.053]	.048 [.045,.051]	.049 [.045,.052]
200	100	100	1.00	.057 [.054,.061]	.048 [.045,.052]	.048 [.044,.051]	.047 [.044,.051]	.048 [.045,.052]
240	120	120	1.00	.061 [.058,.065]	.053 [.049,.056]	.053 [.049,.056]	.052 [.048,.055]	.052 [.049,.056]
80	40	40	1.25	.105 [.099,.111]	.086 [.082,.091]	.077 [.073,.082]	.074 [.070,.078]	.079 [.074,.083]
120	60	60	1.25	.124 [.119,.130]	.103 [.098,.108]	.091 [.086,.095]	.089 [.084,.093]	.091 [.086,.095]
160	80	80	1.25	.142 [.137,.148]	.122 [.117,.128]	.103 [.098,.108]	.104 [.099,.109]	.106 [.101,.111]
200	100	100	1.25	.162 [.156,.168]	.142 [.136,.148]	.124 [.119,.129]	.122 [.117,.128]	.127 [.122,.132]
240	120	120	1.25	.182 [.176,.189]	.162 [.156,.168]	.136 [.131,.142]	.135 [.130,.141]	.139 [.133,.145]
80	40	40	1.50	.194 [.186,.202]	.164 [.158,.170]	.145 [.139,.151]	.143 [.137,.148]	.146 [.140,.151]
120	60	60	1.50	.265 [.258,.273]	.233 [.227,.240]	.194 [.188,.200]	.195 [.189,.202]	.199 [.193,.205]
160	80	80	1.50	.328 [.321,.336]	.298 [.290,.305]	.243 [.236,.250]	.241 [.234,.248]	.246 [.239,.253]
200	100	100	1.50	.393 [.385,.401]	.364 [.356,.371]	.289 [.281,.296]	.290 [.282,.297]	.296 [.288,.303]
240	120	120	1.50	.447 [.439,.455]	.416 [.408,.424]	.331 [.324,.339]	.334 [.327,.342]	.339 [.332,.347]
80	40	40	1.75	.294 [.285,.303]	.260 [.253,.268]	.225 [.218,.232]	.221 [.214,.228]	.227 [.221,.234]
120	60	60	1.75	.424 [.415,.432]	.384 [.376,.392]	.325 [.318,.333]	.321 [.314,.329]	.327 [.320,.335]
160	80	80	1.75	.533 [.525,.541]	.497 [.489,.505]	.408 [.400,.416]	.407 [.399,.415]	.414 [.406,.422]
200	100	100	1.75	.630 [.622,.638]	.596 [.589,.604]	.492 [.484,.500]	.494 [.486,.502]	.499 [.491,.507]
240	120	120	1.75	.709 [.701,.716]	.678 [.670,.685]	.569 [.561,.577]	.575 [.567,.583]	.576 [.568,.584]
80	40	40	2.00	.430 [.420,.440]	.383 [.375,.391]	.320 [.312,.327]	.315 [.308,.323]	.323 [.315,.330]
120	60	60	2.00	.586 [.578,.595]	.543 [.535,.551]	.458 [.450,.466]	.460 [.452,.468]	.462 [.454,.470]
160	80	80	2.00	.719 [.712,.727]	.685 [.677,.692]	.574 [.566,.582]	.579 [.571,.587]	.580 [.572,.588]
200	100	100	2.00	.805 [.799,.812]	.782 [.776,.789]	.676 [.668,.683]	.681 [.673,.688]	.681 [.673,.688]
240	120	120	2.00	.862 [.856,.867]	.846 [.840,.852]	.750 [.743,.757]	.753 [.746,.760]	.756 [.749,.763]
80	40	40	2.25	.534 [.524,.543]	.488 [.480,.496]	.428 [.420,.436]	.421 [.413,.429]	.426 [.418,.434]
120	60	60	2.25	.717 [.709,.724]	.678 [.671,.686]	.588 [.581,.596]	.591 [.583,.599]	.591 [.583,.599]
160	80	80	2.25	.832 [.826,.838]	.809 [.803,.815]	.707 [.700,.715]	.710 [.703,.717]	.712 [.704,.719]
200	100	100	2.25	.905 [.900,.909]	.887 [.882,.892]	.797 [.791,.804]	.801 [.795,.808]	.802 [.795,.808]
240	120	120	2.25	.950 [.946,.953]	.941 [.937,.945]	.873 [.868,.879]	.876 [.871,.881]	.877 [.871,.882]
80	40	40	2.50	.637 [.627,.646]	.588 [.580,.595]	.509 [.501,.517]	.504 [.496,.512]	.508 [.500,.516]
120	60	60	2.50	.816 [.809,.822]	.783 [.776,.789]	.689 [.682,.697]	.694 [.686,.701]	.693 [.685,.700]
160	80	80	2.50	.909 [.904,.913]	.892 [.887,.897]	.807 [.801,.814]	.808 [.802,.815]	.813 [.807,.819]
200	100	100	2.50	.957 [.954,.960]	.948 [.944,.951]	.888 [.882,.893]	.889 [.883,.894]	.891 [.885,.895]
240	120	120	2.50	.983 [.981,.985]	.979 [.977,.982]	.934 [.930,.938]	.936 [.932,.940]	.936 [.932,.940]
80	40	40	2.75	.715 [.706,.724]	.677 [.669,.684]	.597 [.590,.605]	.591 [.583,.599]	.599 [.591,.607]
120	60	60	2.75	.881 [.875,.886]	.856 [.850,.862]	.775 [.768,.782]	.776 [.769,.783]	.777 [.771,.784]
160	80	80	2.75	.952 [.948,.955]	.941 [.937,.945]	.884 [.879,.889]	.886 [.881,.891]	.888 [.882,.893]
200	100	100	2.75	.981 [.979,.983]	.977 [.975,.979]	.937 [.933,.941]	.940 [.936,.944]	.940 [.936,.944]
240	120	120	2.75	.994 [.992,.995]	.992 [.990,.993]	.972 [.969,.975]	.973 [.970,.975]	.974 [.972,.977]
80	40	40	3.00	.781 [.773,.789]	.743 [.736,.750]	.665 [.657,.672]	.660 [.653,.668]	.665 [.657,.673]
120	60	60	3.00	.926 [.922,.930]	.908 [.903,.913]	.841 [.835,.847]	.841 [.835,.847]	.843 [.837,.849]
160	80	80	3.00	.975 [.973,.978]	.968 [.965,.971]	.929 [.925,.933]	.929 [.925,.933]	.930 [.926,.934]
200	100	100	3.00	.992 [.991,.994]	.990 [.988,.992]	.967 [.964,.969]	.968 [.965,.970]	.969 [.966,.972]
240	120	120	3.00	.998 [.997,.999]	.997 [.997,.998]	.987 [.985,.989]	.988 [.986,.989]	.988 [.986,.989]

Point estimates of the statistical power and 95% Wilson confidence intervals are reported

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